You can download and install a new or an older version from this link.
If you no longer have access to your Activation Key,
You can acquire it by submitting the e-mail address you used to purchase the program on this Web Site.
If you no longer have access to the e-mail address you used to purchase the key. You should contact Support to assist you. https://support.techsmith.com/hc/en-us/requests/new
As far as transferring Library contents goes.
You can use the Editors tools to create a "Backup" of those files.
Then, when you have SnagIt installed on the new computer you folow the same steps used to create the backup but chose "Restore".
See Image Below, Click to Enlarge